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QOTD # 14 The perimeter of a flat rectangular lawn is 42 met [#permalink]
10 Sep 2016, 01:50

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Question Stats:

100% (01:34) correct
0% (00:00) wrong based on 11 sessions

The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is 75 percent of its length. What is the area of the lawn, in square meters?

Re: QOTD # 14 The perimeter of a flat rectangular lawn is 42 met [#permalink]
10 Sep 2016, 01:52

Expert's post

Explanation

Let s and t be the width and length, in meters, of the lawn, respectively. Then the perimeter is 25 + 2t meters, so that 2s + 2t = 42. Also, the relationship between the width and the length can be translated as 5 = 0.75t. Substituting 0.75t for s in the equation for the perimeter yields 42 = 2(0.75t) + 2t = 3.5t. So \(t = \frac{42}{3.5}\) and 5 = (0.75)(12) = 9. Since 5t = 108, the area of the lawn is 108 square meters.

Re: QOTD # 14 The perimeter of a flat rectangular lawn is 42 met [#permalink]
19 Sep 2016, 16:50

1

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Expert's post

Carcass wrote:

The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is 75 percent of its length. What is the area of the lawn, in square meters?

A) 40.5 B) 96 C) 108 D) 192 E) 432

The width of the lawn is 75 percent of its length In other words, the width is 3/4 times the length. Let L = the length This means (3/4)L = the width Or we can write 3L/4 = the width

The perimeter of a flat rectangular lawn is 42 meters In other words, 2(length) + 2(width) = 42 So, 2L + 2(3L/4) = 42 Simplify: 2L + 3L/2 = 42 Multiply both sides by 2 to get: 4L + 3L = 84 Simplify: 7L = 84 Solve: L = 12

Since 3L/4 = the width, we know that the width = 3(12)/4 = 9